IDEAS home Printed from https://ideas.repec.org/a/hin/complx/9836150.html
   My bibliography  Save this article

Stochasticity, Selection, and the Evolution of Cooperation in a Two-Level Moran Model of the Snowdrift Game

Author

Listed:
  • Brian McLoone
  • Wai-Tong Louis Fan
  • Adam Pham
  • Rory Smead
  • Laurence Loewe

Abstract

The Snowdrift Game, also known as the Hawk-Dove Game, is a social dilemma in which an individual can participate (cooperate) or not (defect) in producing a public good. It is relevant to a number of collective action problems in biology. In a population of individuals playing this game, traditional evolutionary models, in which the dynamics are continuous and deterministic, predict a stable, interior equilibrium frequency of cooperators. Here, we examine how finite population size and multilevel selection affect the evolution of cooperation in this game using a two-level Moran process, which involves discrete, stochastic dynamics. Our analysis has two main results. First, we find that multilevel selection in this model can yield significantly higher levels of cooperation than one finds in traditional models. Second, we identify a threshold effect for the payoff matrix in the Snowdrift Game, such that below (above) a determinate cost-to-benefit ratio, cooperation will almost surely fix (go extinct) in the population. This second result calls into question the explanatory reach of traditional continuous models and suggests a possible alternative explanation for high levels of cooperative behavior in nature.

Suggested Citation

  • Brian McLoone & Wai-Tong Louis Fan & Adam Pham & Rory Smead & Laurence Loewe, 2018. "Stochasticity, Selection, and the Evolution of Cooperation in a Two-Level Moran Model of the Snowdrift Game," Complexity, Hindawi, vol. 2018, pages 1-14, February.
    • Handle: RePEc:hin:complx:9836150
    DOI: 10.1155/2018/9836150
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2018/9836150.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2018/9836150.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2018/9836150?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. , H., 2010. "Orders of limits for stationary distributions, stochastic dominance, and stochastic stability," Theoretical Economics, Econometric Society, vol. 5(1), January.
    2. Shpak, Max & Orzack, Steven Hecht & Barany, Ernest, 2013. "The influence of demographic stochasticity on evolutionary dynamics and stability," Theoretical Population Biology, Elsevier, vol. 88(C), pages 47-56.
    3. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    4. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    5. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    6. Frey, Erwin, 2010. "Evolutionary game theory: Theoretical concepts and applications to microbial communities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(20), pages 4265-4298.
    7. Bernhard Voelkl, 2010. "The ‘Hawk-Dove’ Game and the Speed of the Evolutionary Process in Small Heterogeneous Populations," Games, MDPI, vol. 1(2), pages 1-14, May.
    8. Jeff Gore & Hyun Youk & Alexander van Oudenaarden, 2009. "Snowdrift game dynamics and facultative cheating in yeast," Nature, Nature, vol. 459(7244), pages 253-256, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hong, Le & Wang, Ruihan & Chen, Hao & Cui, Weicheng & Tsoulakos, Nikolaos & Yan, Ran, 2025. "Evolutionary game-based ship inspection planning considering ship competitive interactions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 196(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Van Cleve, Jeremy, 2015. "Social evolution and genetic interactions in the short and long term," Theoretical Population Biology, Elsevier, vol. 103(C), pages 2-26.
    2. Du, Faqi & Fu, Feng, 2013. "Quantifying the impact of noise on macroscopic organization of cooperation in spatial games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 35-44.
    3. Alex McAvoy & Christoph Hauert, 2015. "Asymmetric Evolutionary Games," PLOS Computational Biology, Public Library of Science, vol. 11(8), pages 1-26, August.
    4. Zhang, Shuai & Clark, Ruaridh & Huang, Yunke, 2020. "Frequency-dependent strategy selection in a hunting game with a finite population," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    5. Cao, Lixuan & Wu, Bin, 2021. "Eco-evolutionary dynamics with payoff-dependent environmental feedback," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Qi Su & Lei Zhou & Long Wang, 2019. "Evolutionary multiplayer games on graphs with edge diversity," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-22, April.
    7. Ohdaira, Tetsushi, 2024. "The universal probabilistic reward based on the difference of payoff realizes the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    8. Sergio Currarini & Carmen Marchiori & Alessandro Tavoni, 2016. "Network Economics and the Environment: Insights and Perspectives," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(1), pages 159-189, September.
    9. Kroumi, Dhaker & Martin, Éloi & Lessard, Sabin, 2022. "Evolution of cooperation with respect to fixation probabilities in multi-player games with random payoffs," Theoretical Population Biology, Elsevier, vol. 145(C), pages 1-21.
    10. Yali Dong & Cong Li & Yi Tao & Boyu Zhang, 2015. "Evolution of Conformity in Social Dilemmas," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-12, September.
    11. Te Wu & Feng Fu & Long Wang, 2011. "Moving Away from Nasty Encounters Enhances Cooperation in Ecological Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 6(11), pages 1-7, November.
    12. Flávio L Pinheiro & Jorge M Pacheco & Francisco C Santos, 2012. "From Local to Global Dilemmas in Social Networks," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-6, February.
    13. Jorge Peña & Yannick Rochat, 2012. "Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-13, September.
    14. Cheng, Jiangjiang & Mei, Wenjun & Su, Wei & Chen, Ge, 2023. "Evolutionary games on networks: Phase transition, quasi-equilibrium, and mathematical principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    15. Qinghu Liao & Wenwen Dong & Boxin Zhao, 2023. "A New Strategy to Solve “the Tragedy of the Commons” in Sustainable Grassland Ecological Compensation: Experience from Inner Mongolia, China," Sustainability, MDPI, vol. 15(12), pages 1-24, June.
    16. Charles G Nathanson & Corina E Tarnita & Martin A Nowak, 2009. "Calculating Evolutionary Dynamics in Structured Populations," PLOS Computational Biology, Public Library of Science, vol. 5(12), pages 1-7, December.
    17. Li, Minlan & Wang, Chao & Han, Yanyan & Wang, Si-Yi & Wang, Ruiwu, 2025. "Environmental feedback promotes cooperation in a spatial prisoner's dilemma game with preferential selection," Applied Mathematics and Computation, Elsevier, vol. 495(C).
    18. Wang, Chaoqian & Huang, Chaochao, 2022. "Between local and global strategy updating in public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    19. Wang, Weijie & Xu, Zhehang & Hua, Shijia & Cui, Longqing & Zhang, Jianlin & Meng, Fanyuan, 2024. "Threshold-initiated spatial public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    20. Egas, Martijn & Riedl, Arno, 2005. "The Economics of Altruistic Punishment and the Demise of Cooperation," IZA Discussion Papers 1646, Institute of Labor Economics (IZA).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:9836150. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.